Quantum and Classical Integrable Systems

The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the universal enveloping algebra of an affine Lie algebra, or its q-deformation.) A similar relation also holds in the classical case. We discuss different guises of this very important relation and its implication for the description of the spectrum and the eigenfunctions of the quantum system. Parallels between the classical and the quantum cases are thoroughly discussed.Comment: 59 pages, LaTeX2.09 with AMS symbols. Lectures at the CIMPA Winter School on Nonlinear Systems, Pondicherry, January 199

Density-Dependence of Two-Body Interactions Beyond the Mean-Field Approximation. Part 1: Generalized Brueckner G-Matrix in the Local Approximation

This paper has been merged with the preprint nucl-th/0210057. The combined version is accepted for publication is Phys. Rev. CComment: This paper has been merged with the preprint nucl-th/0210057. The combined version is accepted for publication is Phys. Rev.